A gentle introduction to Measure Theory

Arc Spaces , Motivic Integration

The concept ofmotivic integrationwas invented by Kontsevich to show that birationally equivalent Calabi-Yau manifolds have the same Hodge numbers. He constructed a certain measure on the arc space of an algebraic variety, the motivic measure, with the subtle and crucial property that it takes values not in R, but in the Grothendieck ring of algebraic varieties. A whole theory on this subject wa...

A Gentle Introduction to the Kernel Distance

This document reviews the definition of the kernel distance, providing a gentle introduction tailored to a reader with background in theoretical computer science, but limited exposure to technology more common to machine learning, functional analysis and geometric measure theory. The key aspect of the kernel distance developed here is its interpretation as an L2 distance between probability mea...

Arc Spaces, Motivic Integration and Stringy Invariants

The concept of motivic integration was invented by Kontsevich to show that birationally equivalent Calabi-Yau manifolds have the same Hodge numbers. He constructed a certain measure on the arc space of an algebraic variety, the motivic measure, with the subtle and crucial property that it takes values not in R, but in the Grothendieck ring of algebraic varieties. A whole theory on this subject ...

Set Theory in Computer Science A Gentle Introduction to Mathematical Modeling

Microlocal Studies of Shapes

A gentle introduction to stratified Morse theory and Kashiwara’s conormal cycle.